1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Limit rational function without L'H

  1. Mar 15, 2013 #1
    1. The problem statement, all variables and given/known data
    evaluate.


    2. Relevant equations
    [itex]lim_{x->0+} \frac{\sqrt{x}}{\sqrt{sinx}}[/itex]


    3. The attempt at a solution
    i've tried l'hopital's and it is just endless cycle.
     
  2. jcsd
  3. Mar 15, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    It's the same as sqrt(x/sin(x)). You know the limit of x/sin(x), right?
     
  4. Mar 15, 2013 #3

    Mark44

    Staff: Mentor

    Sometimes, L'Hopital's Rule is not the way to go. Under the right conditions, you can switch the order of the limit operation and the function in the limit.
    ## \lim f(g(x)) = f(\lim g(x))##

    Also, as long as all quantities are positive,
    $$ \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$$
     
  5. Mar 15, 2013 #4
    yes, but it is of the form 0/0.
     
  6. Mar 15, 2013 #5

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    That doesn't mean you HAVE to use l'Hopital. You know the limit of x/sin(x), use l'Hopital on that. Then take the square root. Use that the square root is continuous for positive arguments.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Limit rational function without L'H
Loading...